Quantum and Kinetic Transport: Analysis, Computations, and New Applications

Overview

We are at the dawn of the nanotechnology era, where scientific and technological advancements in many fields strongly demand the investigation of problems involving small or multiple scales. In such problems, the hydrodynamic theory is often invalid, and one has to apply the more fundamental laws of physics, such as kinetic theory (Boltzmann equation), molecular dynamics (Newton’s second law or the Liouville equation), or even quantum mechanics (Schrodinger equation). This requires the development of new mathematical and computational methods for physical laws at these scales, or a mixture of them, which is facilitated by the improvements of modern computers. Mathematical understanding of the scaling limit from one scale to another plays an important role, and interweaves with the development of new multiscale computational methods. This program will focus on the mathematical analysis, computational challenges and new applications of quantum and kinetic transport theory. It will invite both senior leading figures and young researchers in these directions. Besides applied mathematicians, special attention will be paid to invite researchers in other fields in science and engineering, representing academic, national lab and industrial research.